Stress-gradient induced migration of polymers in corrugated channels

Abstract

We study the flow of a dilute polymer solution in a wavy channel under steady-state flow conditions by employing the nonequilibrium thermodynamics two-fluid model [Mavrantzas and Beris, Phys. Rev. Lett. 69, 273–276 (1992)], allowing for the coupling between polymer concentration and polymer stresses. The resulting highly complex system of partial differential equations describing inhomogeneous transport phenomena in the fluid are solved with an efficient implementation of the mixed finite-element method. We present numerical results for polymer concentration, stress, velocity, and fluxes of polymer as a function of the nondimensional parameters of the problem (the Deborah number De, the Peclet number Pe, the Reynolds number Re, the ratio of the solvent viscosity to the total fluid viscosity β, and the constriction ratio of the channel width cr). We find that the constricted part of the wall is depleted of polymer, when the polymer diffusion length scale, expressed by the ratio of De/Pe, increases. The migration is more pronounced for macromolecules characterized by longer relaxation times and takes place toward the expanding part of the channel or toward the centerplane. Migration is also enhanced by the width variability of the channel: The more corrugated the channel, the stronger the transfer of polymer to the centerplane. This increases the spatial extent of polymer depletion near the wall or induces a zone of sharp variation in polymer stress and concentration, which moves away from the channel wall, especially in lower polymer concentration. The development of a polymer-depleted layer smooths out the boundary layer which is known to arise with Boger fluids at the walls of such corrugated channels or tubes and gives rise to an “apparent” slip in the constricted section of the wall and to a very low value of the drag force on the wall. When and where boundary layers arise, they scale as (1/De) for the stresses and as (De/Pe)1/3 for the concentration.

On the velocity discontinuity at a critical volume of a bubble rising in a viscoelastic fluid

“…Considering that the stress tensor is related to the conformation tensor via Kramers' relation (Tsouka et al 2014), it can be said that its trace corresponds to the degree to which the viscoelastic medium has been stretched (Chilcott & Rallison 1988). When network elements reach the rear pole of the bubble, their instant configuration becomes highly stretched (birefringent pipe, Malaga & Rallison (2007)), see figure 7(a).…”

Molecular-scale simulation of cross-flow migration in polymer melts

“…There are just a few simulation studies of segregation effects in dense polymer melts and these are limited to bidisperse melts at reduced densities [12,13]; only one of these studies incorporates flow effects [13]. Similarly, while theoretical developments have progressed for dilute solutions [14][15][16], results are sparse for melts [17,18]. Despite the fundamental interest and technological importance, no simulation studies on polydisperse melts have appeared in the literature, presumably due to the computational complexity.…”

Hemodynamics in stenotic vessels of small diameter under steady state conditions: Effect of viscoelasticity and migration of red blood cells

“…This boundary condition is required because of the inclusion of the term ∇ 2 τ in Eq. 17, unlike the models employed by Beris and Mavrantzas [29] and Tsouka et al [44]. There is no mass flux of the RBCs across the wall:…”